On the Relationship between Parsimonious Covering and Boolean Minimization

Minimization of Boolean switching functions is a basic problem in the design of logic circuits. The designer first comes up with a switching funct.ion expressed in terms of several binary input. variables that satisfies tlie desired functionality, and then attempts t.0 minimize the function as a sum of products or product of sums. It turns out that a sum of products form of a switching function that has no redundancy is a union of prime implicnnis of the function. In this paper we would like to esplicat,e some of the relationships of the boolean minimization problem to a formalization of obduclive inference called pcirsirn 071 i o us couering . Abductive inference ofteti occurs i n diagnostic problems suc l i as fiiiditig the ca.uses of circuit faults [Reiter, 871 or determining the diseases causing t,he symptoms reported by a pat ient [Peng and Reggia, 901. Pa,rsimonious covering involves covering all observed facts by means of a parsimonious set of explana'This research was supported in part by the State of Ohio Research Challengegrants to both the aut.liow, arid in part. by the NSF grant IRI-9009587 to the second aut,hor. 1164 tions that can account for the observa.tions. The relationship of parsimonious covering to boolean minimization has been noted by the developers of the theory; we intend to pursue a detailed mapping here.